What is (\partial)/(\partial z)(4xln(y)+yln(z)-x) ?

The answer to (\partial)/(\partial z)(4xln(y)+yln(z)-x) is y/z

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(\partial)/(\partial z)(4xln(y)+yln(z)-x)

\frac{\partial}{\partial z} (4 x ln (y) + y ln (z) - x)

\frac{y}{z}

Solution steps

\frac{\partial}{\partial z} (4 x ln (y) + y ln (z) - x)

Treat

x, y

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial z} (4 x ln (y)) + \frac{\partial}{\partial z} (y ln (z)) - \frac{\partial}{\partial z} (x)

\frac{\partial}{\partial z} (4 x ln (y)) = 0

\frac{\partial}{\partial z} (y ln (z)) = \frac{y}{z}

\frac{\partial}{\partial z} (x) = 0

= 0 + \frac{y}{z} - 0

Simplify

= \frac{y}{z}

(x - 4 y - 3) d x - (x - 6 y - 5) d y = 0

n \to \infty lim (cos (n))

x \to 0 lim (\frac{( sin ( 9 x ) )}{x})

f (x) = (x^{2} + 9 x + 2)^{5}

f (x) = 2 e^{x} + 10 x, at x = 0

What is (\partial)/(\partial z)(4xln(y)+yln(z)-x) ?
The answer to (\partial)/(\partial z)(4xln(y)+yln(z)-x) is y/z